Advanced Dose-Level Quantization for Multibeam-Writers

ABSTRACT

In a charged-particle multi-beam writing method a desired pattern is written on a target using a beam of energetic electrically charged particles, by imaging apertures of a pattern definition device onto the target, as a pattern image which is moved over the target. Thus, exposure stripes are formed which cover the region to be exposed in sequential exposures, and the exposure stripes are mutually overlapping, such that each area of said region is exposed by at least two different areas of the pattern image at different transversal offsets (Y 1 ). For each pixel, a corrected dose amount is calculated by dividing the value of the nominal dose amount by a correction factor (q), wherein the same correction factor (q) is used with pixels located at positions which differ only by said transversal offsets (Y 1 ) of overlapping stripes.

RELATED APPLICATION

This application claims priority to U.S. provisional patent applicationSer. No. 62/451,528 entitled “Advanced Dose-Level Quantization forMultibeam-Writers” filed on Jan. 27, 2017, which is incorporated hereinby reference.

FIELD OF THE INVENTION

The invention generally relates to methods and apparatuses forgenerating a desired pattern on a specified target by irradiating atarget with a beam of energetic radiation formed by electrically chargedparticles.

BACKGROUND OF THE INVENTION

The use of charged particle beams in the field of generating desiredpatterns such as for example those found on printed circuit boards iswell known. One common technique for generating such patterns uses aMultibeam-Writer (MBW) which projects a charged particle beam through aseries of apertures onto a desired surface. Such devices typicallyemploy charged-particle optics systems, Pattern Definition (PD) devices,and a variety of methods for creating the ultimate pattern on thedesired target surface.

In typical MBW systems the charged particle beam is moved along apredetermined path with respect to a target area, upon which a desiredimage is thereby created.

BRIEF SUMMARY OF THE INVENTION

Systems and methods in accordance with various embodiments of theinvention provide a multibeam-writing system which projects a chargedparticle beam through a series of apertures onto a target area andmethods for improving the clarity of the final desired pattern. In anumber of embodiments the methods providing a pattern definition devicehaving a plurality of apertures transparent to a source of radiation,and directing an illuminating wide beam through the apertures of thepattern definition device to form a patterned beam consisting of acorresponding plurality of beamlets, and illuminating a target with thepatterned beam during a sequence of exposure intervals to form a patternimage on the target, wherein the pattern image further comprises aplurality of pattern pixels located on the target wherein the pluralityof pattern pixels correspond to at least a portion of the plurality ofapertures, and wherein during the sequence of exposure intervals, the atleast a portion of the plurality of apertures are selectively controlledsuch that the plurality of pattern pixels are exposed to a respectivedose amount in accordance with the desired pattern, generating arelative movement between the target and the pattern definition deviceto produce a stepwise movement of the pattern image on the target alonga path over an exposure region, said path comprising a pluralitysections which extend along a scanning direction, wherein the pluralityof sections correspond to a plurality of exposure stripes thatcollectively cover the entirety of said exposure region over sequentialexposures, wherein the exposure stripes are mutually overlapping andoffset from each other in a direction transverse to the scanningdirection, such that exposure region is exposed by at least twodifferent exposure stripes at different transversal offsets, andcalculating, for each pixel, a corrected dose amount by dividing thevalue of the nominal dose amount by a correction factor, wherein thesame correction factor is used with pixels written by beamlets locatedat positions which differ only by said transversal offsets ofoverlapping stripes.

In other embodiments the method further provides that wherein during thestep of calculating a corrected dose amount for each pixel, an availablecurrent density at the respective pixel is determined, wherein saidmaximum available current density is determined as the actual currentdensity of the irradiating beam radiated through the aperturecorresponding to the respective pixel, said correction factor of therespective pixel is calculated as the ratio of said available currentdensity to the minimum current density across the overall beam arrayfield, and correction factors are averaged among those pixels that arelocated at positions which differ only by said transversal offsets ofoverlapping stripes.

In yet other embodiments the further provides multiplicativerenormalization of the correction factors, using a renormalizing factorchosen such that one of the largest value and the smallest value of thecorrection factors is renormalized to 1.

In still other embodiments the method provides that step of calculatinga corrected dose amount for each pixel comprises calculating, for eachpixel in a row of pixels parallel to the scanning direction within arespective exposure stripe, corrected dose amounts by dividing thevalues of the dose amounts by a row correction factor, wherein said rowcorrection factor is uniformly applied to all pixels of a row of pixels.

In yet still other embodiments the method provides that said rowcorrection factor is calculated for a respective row of pixels based onthe values of current dose actually radiated through a series ofapertures, said series of apertures containing all apertures within thepattern definition device which impart dose amounts to the respectiverow of pixels, wherein the row correction factor of a row of pixels iscalculated as the ratio of actual current dose of an aperture, asaveraged over the corresponding series of apertures, to a nominalcurrent dose value assumed to be constant over the plurality ofapertures of the pattern definition device.

In even other embodiments the method provides that said region where abeam exposure is to be performed is composed of a plurality of patternpixels arranged in a regular arrangement, said region having a totalwidth as measured across said scanning direction, said exposure stripeswithin said region running substantially parallel to each other alongsaid scanning direction and having uniform widths as measured acrosssaid scanning direction.

In other embodiments the method provides that the exposure stripes aremutually overlapping, the position of the stripes differing by atransversal offset in a direction across the scanning direction, whereinthe row correction factors of rows of pixels are averaged over thoserows of pixels which are offset to each other by said transversaloffset.

In still other embodiments the method provides that the correctionfactor varies between groups of pixels where said groups of pixelsdiffer by an offset which does not correspond to a transversal offset ofoverlapping stripes.

In yet other embodiments the method further provides computing anexposure pattern suitable for exposing the desired pattern on a targetusing said pattern definition device for writing said desired pattern byexposing a multitude of pixels within said region on the target, whereinduring exposing the desired pattern on a target: in said patterndefinition device said plurality of blanking apertures is arranged in apredetermined arrangement defining mutual positions of the blankingapertures, each blanking aperture being selectively adjustable withregard to a dose value to be exposed through the respective blankingaperture onto a corresponding aperture image on the target during arespective exposure interval, said dose value taking a respective valuein accordance with a discrete palette, said discrete palette including anumber of gray values forming a scale ranging from a minimum value to amaximum value, during a writing process of said desired pattern, asequence of exposure intervals is made, wherein in each exposureinterval the blanking apertures are imaged onto the target, thusgenerating a corresponding plurality of aperture images, wherein theposition of aperture images is kept fixed relative to the target at theposition of a pixel during an exposure interval, but between exposureintervals the position of aperture images is shifted over the target,thus exposing the multitude of pixels on the target, and the apertureimages are mutually overlapping on the target, and the aperture imageshave a nominal width which is greater than the distance between pixelpositions of neighboring aperture images on the target, by anoversampling factor greater than one, wherein computing the exposurepattern comprises: determining the discrete palette, providing thedesired pattern and calculating a nominal exposure pattern as a rastergraphics defined on the multitude of pixel elements, said nominalexposure pattern being suitable to create a nominal dose distribution onthe target realizing contour lines of the desired pattern and includingfor each pixel element a respective nominal dose value, and determining,for each pixel element, a discrete value which approximates the nominaldose value of the respective pixel element, said discrete value beingselected from the discrete palette, wherein determining the discretevalues includes employing ordered dithering using a dither matrix of apredefined size.

In yet still other embodiments the method provides that the dithermatrix is a Bayer matrix.

In even other embodiments a pattern definition device is providedcomprising: a plurality of apertures transparent to a source ofradiation, a data processing unit having at least one input terminal andin communication with the plurality of apertures transparent to a sourceof radiation wherein the data processing unit is configured to receive aset of instructions defining a desired pattern image to be exposed on atarget area, wherein at least a portion of the plurality of aperturescorrespond to a plurality of pattern image pixels on the target area andthe at least a portion of the plurality of apertures are configured toexpose the pattern image pixels to a respective dose amount inaccordance with the desired pattern image, and wherein the dataprocessing is further configured to calculate a correction needed foreach of the pattern image pixels to correct for a pattern beam overlapby dividing a value of the nominal dose amount by a correction factordose, and wherein the data processing unit is further configured tocommunicate the correction dose to the plurality of apertures.

BRIEF DESCRIPTION OF THE DRAWINGS

The description will be more fully understood with reference to thefollowing figures, which are presented as exemplary embodiments of theinvention and should not be construed as a complete recitation of thescope of the invention, wherein:

FIG. 1 illustrates an MBW system according to the state of the art in alongitudinal sectional view.

FIG. 2 illustrates a cross section view of an Aperture Array Plate inaccordance with prior art for MBW systems.

FIG. 3 illustrates a writing strategy on a target using stripes arrangedalong a common scanning direction in accordance with prior artteachings.

FIG. 4 Illustrates an example of a pixel map of an exemplary pattern tobe exposed in accordance with prior art teachings.

FIG. 5 Illustrates an arrangement of apertures as imaged onto a targetin accordance with prior art teachings.

FIG. 6A illustrates an arrangement of apertures in accordance with priorart teachings.

FIG. 6B illustrates an example oversampling of the pixels in a “doublegrid” arrangement.

FIG. 7 illustrates an exemplary embodiment of an exposure scheme ofpixels of one stripe in accordance with prior art teachings.

FIGS. 8A and 8B illustrate the overlapping stripe (“multi-pass”)strategy for the example of two passes in accordance with manyembodiments.

FIG. 9A illustrates an intensity profile and a dose level in accordancewith various embodiments.

FIG. 9B illustrates another view of an intensity profile in accordancewith various embodiments.

FIGS. 9C and 9D illustrate MBW intensity profiles and related data asobtained for a simulation of a line in accordance with many embodiments.

FIG. 10 illustrates an intensity profile generated by exposure of asingle exposure spot in accordance with many embodiments

FIG. 11A illustrates an intensity profile generated from the exposure ofa line of a determined width.

FIGS. 11B and 11C illustrate the fine adjustment of the position of oneedge (FIG. 11B) or both edges (FIG. 11C) of the line of FIG. 11A viasuitable modifications of the dose levels corresponding the exposurespots.

FIG. 12 illustrates an example of a measured current density map inaccordance with many embodiments.

FIG. 13 is illustrative of an exemplary embodiment of a data path of anMBW.

FIG. 14 illustrates an exemplary embodiment of double-grid oversampling.

FIG. 15 illustrates possible configurations of dose in accordance withvarious embodiments.

FIG. 16 illustrates an embodiment of dithering with o=2.

FIG. 17A illustrates the index matrix used in the dithering matrix inaccordance with FIG. 16.

FIG. 17B illustrates the threshold matrix used in the dithering matrixin accordance with FIG. 16.

FIG. 18 illustrates an embodiment of dithering with o=4.

FIG. 19A illustrates the index matrix used in the dithering matrix inaccordance with FIG. 18.

FIG. 19B illustrates the threshold matrix used in the dithering matrixin accordance with FIG. 18

FIG. 20 illustrates an exemplary embodiment of the dithering process.

FIG. 21 illustrates another exemplary embodiment of the ditheringprocess.

FIG. 22 illustrates an exemplary embodiment of the dithering processfurther illustrating a correction of beam current inhomogeneity.

FIG. 23 illustrates an exemplary embodiment further illustrating acorrection of beam current inhomogeneity which is uniform along thescanning direction.

FIGS. 24 and 25 illustrate other exemplary embodiments of dithering inaccordance with the invention.

FIG. 26 illustrates a plot of the rounding error as a function of thenominal target dose.

FIG. 27A shows an exemplary embodiment of a typical current profileacross an image field.

FIG. 27B shows the current profile of FIG. 27A averaged along theX-direction

FIG. 28A shows correction dose factors for the current profile of FIG.27A

FIG. 28B shows correction dose factors for a uniform correction, i.e.uniform along the X-direction.

FIG. 29A shows the corrected dose profile as obtained from FIGS. 27A and28A.

FIG. 29B shows the corrected dose profile as obtained from FIGS. 27B and28B.

FIGS. 30A to 32B show current profiles, correction dose factors andcorrected dose profiles in a manner analogous to FIGS. 27A to 29B,respectively, in accordance with various embodiments of the invention.

FIGS. 33A to 35B show current profiles, correction dose factors andcorrected dose profiles in a manner analogous to FIGS. 27A to 29Brespectively in accordance with various embodiments of the invention.

DETAILED DESCRIPTION

Turning now to the description and drawings, methods and apparatus forimproving a multibeam-writing systems are provided. In many embodimentsof a multibeam-writer, a charged-particle beam is directed onto adesired target area as the beam device moves in relation to the targetarea. In such embodiments, a desired pattern is translated onto thetarget as the charged particle beam passes through a series of imagingapertures and/or subsequent lenses and deflectors that direct the beamonto the target in the desired positions (i.e. pixel locations) as thedevice is moved over the target area. In various embodiments exposurestripes are formed over the region to be exposed as the device moves;creating mutually overlapping exposure areas from each subsequent pass.In embodiments, at each desired pixel location correction factors areapplied to account for image blurring from the exposure stripe overlap.

A typical implementation of a Multibeam-Writer (MBW) utilizes a 50 keVelectron writer tool resulting in a total beam size of 20 nm whichcomprises a 512×512 grid of 262,144 total programmable beamlets within abeam array field of 81.92 μm×81.92 μm at the target area. An MBW of thistype typically utilizes a 152.4 mm×152.4 mm substrate that isapproximately 6.35 mm thick. The substrate is typically covered in anelectron beam sensitive resist.

Beam size can be reduced from the typical 20 nm to 10 nm through avariety of changes. Reducing the beam size from 20 to 10 nm cantypically be achieved by using a different aperture array plate (AAP),with 2 μm×2 μm opening size of the apertures instead of 4 μm×4 μmopening size. As outlined in U.S. Pat. No. 8,546,767, whose disclosureis incorporated herein by reference, a change of the beam size may alsobe realized in-situ by spatial adjustment of the AAP having multipleaperture arrays of different geometric parameters, such a total size,aperture spacing, aperture shapes etc.

Even with the reduction of beam size typical overlapping and column blurcan occur. For example, a 10 nm beam size and a substrate with a currentdensity of 4 A/cm², would produce a maximum individual beamlet currentof 1.05 μA for each of the 262,144 programmable beamlets; if allbeamlets were activated. This example would still produce a 1 sigma blurof the column.

First generation MBW production machines use 20 nm and 10 nm beamsproviding up to approximately 1 μA current for all 262,144 programmablebeamlets. New MBW production machines use even smaller beam size. Insome cases, an 8 nm beam size would provide a 640×640 array with 409,600beamlets within the 81.92 μm×81.92 μm beam array field at the substrate.Keeping the maximum current density at 4 A/cm² will ensure that themaximum current (with all beamlets “on”) is 1.05 μA. In other cases, a 5nm beam size would provide a 1024×1024 array equaling 1,048,576programmable beamlets at the substrate; again, at a maximum currentdensity of 4 A/cm² the maximum current (with all beamlets “on”) is 1.05μA.

In many applications the MBW performance becomes increasingly moredemanding as the Critical Dimension requirements become increasinglysmaller for example at the nanometer level. In some applications LocalCritical Dimension Uniformity (LCDU) and Global Critical DimensionUniformity (GCDU) are required to be within a 3 sigma or 6 sigmavariation at the nanometer level over the entire MBW writing field.

Therefore, it is desirable to finely-adjust the line edge position bymeans of a specifically adapted exposure dose profile. Such afine-adjustment should not only be adaptable within the MBW beam arrayfield (local) but also over the whole MBMW writing field on a substrate(global). However, in order to fulfill the very demanding MBWspecifications of very low LCDU and GCDU values, there is the need foradditional fine corrections. Here, the terms “local” and “global” referagain to small fields (e.g. the area of the MBW beam array field) andthe whole MBW writing field on a substrate, respectively.

In addition to the blurring and clarity issues the use of MBWs ofteninvolves the use of exposure stripes for which an effect called“substripes” typically occurs which can affect the overall clarity ofthe projected image. Essentially the beamlets may be affected byimperfections arising from spatial variations in the current densitywithin the beam illuminating the Aperture Array Plate (AAP).Additionally, imperfections in the AAP may contribute to the substripes.Consequently, there is a need to allow for crisper line creation and thereduction of substripes.

Such clarity issues as previously discussed may be corrected inaccordance with the various embodiments described herein.

According to an exemplary embodiment of the invention, it is possible tocorrect the “substripe” effect by applying a correction factor to thenominal dose amounts at the pixels, where the presence of overlappingstripes is taken into account by averaging of the correction factors.More specifically where the exposure stripes mutually overlap in thetransvers direction to the scanning direction the corrected dose factorcan be calculated. The desired image pattern will produce a number ofimage pixels that correspond to a variety of apertures. The pixelsrequired the corrected dose amount calculated based on the substripeoverlap wherein the corrected dose for each pixel is calculated bydividing the value of the nominal dose by a correction factor for eachpixel. The same correction factor may be used for pixels that haveequivalent positions with respect to the mutually overlappingsubstripes. Otherwise the correction factor may, in general, vary, inparticular between pixels (or groups of pixels) which do not haveequivalent positions.

In accordance with one embodiment of the invention, the correctionfactors are calculated to correct variations of the current densitywithin the irradiating beam. Thus, during the step of calculating acorrected dose amount for each pixel, the following steps may beperformed:

-   -   an available current density at the respective pixel is        determined, wherein said available current density is determined        as the actual current density of the irradiating beam radiated        through the aperture corresponding to the respective pixel;    -   the correction factor of the respective pixel is calculated as        the ratio of said available current density to the minimum        current density across the overall beam array field; and    -   an averaging of correction factors is made within respective        sets of pixels, namely by averaging the correction factors among        those pixels that are located at positions which differ with        respect to the transversal offsets of overlapping stripes.

Optionally, a multiplicative renormalization of the correction factors,in particular the averaged correction factors, may be added, forinstance such that the largest or, preferably, the smallest (averaged)correction factor is set to 1.

A further development of this method extends the range of averaging toan entire row of pixels. Thus, in this case the step of calculating acorrected dose amount for each pixel would comprise calculating, foreach pixel in a row of pixels parallel to the scanning direction withina respective exposure stripe, corrected dose amounts by dividing thevalues of the dose amounts by a row correction factor, wherein said rowcorrection factor is uniformly applied to all pixels of a row of pixels.Additionally, the row correction factor may be calculated for arespective row of pixels based on the values of current dose actuallyradiated through a series of apertures. Such a series of apertures maycontain all apertures within the pattern definition device which impartdose amounts to the respective row of pixels. The row correction factorof a row of pixels is calculated as the ratio of actual current dose ofan aperture averaged over the corresponding series of apertures, where anominal current dose value assumed to be constant over the plurality ofapertures of the pattern definition device.

Another embodiment of the invention may be directed to the region wherea beam exposure is to be performed. Such embodiment may comprise of aplurality of pattern pixels arranged in a regular arrangement, saidregion having a total width as measured across said scanning direction.Additionally, the exposure stripes within said region will runsubstantially parallel to each other along said scanning direction andhave uniform widths as measured across the scanning direction. A typicalimplementation of this embodiment may provide that exposure stripes aremutually overlapping, the position of the stripes differing by atransversal offset in a direction across the scanning direction; in thiscase it may be suitable to average row correction factors of rows ofpixels over those rows of pixels which are offset to each other by saidtransversal offset.

Another exemplary embodiment, which further improves avoiding the“substripe” effect and similar rasterizing effects, relates to computingan exposure pattern which is suitable for exposing a desired pattern ona target in a charged-particle lithography apparatus as mentioned above.During the exposure of the desired pattern on the target, a particlebeam is directed to and illuminates a pattern definition devicecomprising an aperture array composed of a plurality of blankingapertures through which said particle beam penetrates for writing saiddesired pattern by exposing a multitude of pixels within a region(region of exposure) on the target. In the pattern definition device,the plurality of blanking apertures are arranged in a predeterminedarrangement defining mutual positions of the blanking apertures. Each ofthe various apertures selectively adjustable with regard to a dose valueto be exposed through the respective blanking aperture onto acorresponding aperture image on the target during a respective exposureinterval. The dose value is a respective value in accordance with adiscrete palette, where the palette includes a number of gray valuesforming a scale ranging from a minimum value to a maximum value. Duringa writing process of the desired pattern, a sequence of exposureintervals is made, wherein in each exposure interval the blankingapertures are imaged onto the target, thus generating a correspondingplurality of aperture images. The position of aperture images is therebykept fixed relative to the target at the position of a pixel during anexposure interval. However, between exposure intervals the position ofaperture images is shifted over the target, thus exposing the multitudeof pixels on the target; and the aperture images are mutuallyoverlapping on the target. The nominal width of the aperture image istypically greater than the distance between pixel positions ofneighboring aperture images on the target, by an oversampling factorgreater than one. In this context, according to the various embodiments,computing the exposure pattern comprises:

-   (i) determining the discrete palette,-   (ii) providing the desired pattern and calculating a nominal    exposure pattern as a raster graphics defined on the multitude of    pixel elements, said nominal exposure pattern being suitable to    create a nominal dose distribution on the target realizing contour    lines of the desired pattern and including for each pixel element a    respective nominal dose value, and-   (iii) determining, for each pixel element, a discrete value (h)    which approximates the nominal dose value of the respective pixel    element, said discrete value being selected from the discrete    palette,-   wherein in step (iii), determining the discrete values includes    employing ordered dithering using a dither matrix, for instance a    Bayer matrix, of a predefined size.

Compared to other dithering methods, ordered dithering has severaladvantages in context of a charged particle multibeam writer. Firstly,it is computationally inexpensive which is highly important for a fast(i.e. real-time) data processing in the data-path. Secondly, it is adeterministic procedure, which means that its results are uniquelyreproducible. Thirdly, the ordered dithering matrix can be chosen (i.e.optimized) in a way such that line edge placement and line edgeroughness in specific directions becomes optimal. This is particularlyuseful since the layout of semi-conductor devices mainly have twopreferred (orthogonal) axes, i.e. usually horizontal and vertical linesare more important and dominant as compared to lines in arbitrarydirection.

Further details of the aforementioned embodiments of a novel dose-levelquantization method for pixel data, as part of the on-line data path ofa lithographic charged particle multibeam exposure tool are discussed inthe subsequent sections.

Various aspects of the multibeam exposure tool are further discussed inU.S. Pat. No. 6,768,125 and U.S. Pat. No. 7,781,748, whose disclosuresare incorporated herein by reference.

Lithographic Apparatus

An overview of a lithographic apparatus suitable to employ exemplaryembodiments of the invention is illustrated in FIGS. 1 and 2. Inaccordance with many embodiments the lithographic apparatus asillustrated in FIG. 1 may comprise an illumination system 3 coupled to aPattern Definition (PD) system 4 which focuses the beam through aprojecting system 5 onto a target station 6. The target stationgenerally contains a substrate for which the projected image is to bedirected to.

In many embodiments the illumination system 3 comprises, for instance,an electron gun 7, an extraction system 8 as well as a condenser lenssystem 9. It should, however, be noted that in place of electrons, ingeneral, other electrically charged particles can be used as well. Apartfrom electrons these can be, for instance, hydrogen ions or heavierions, charged atom clusters, or charged molecules.

The extraction system 8 accelerates the particles to a defined energy oftypically several keV, e.g. 5 keV. By means of a condenser lens system9, the particles emitted from the illumination source 7 are formed intoa broad, substantially telecentric particle beam 50 serving asLithography Beam 19 a. The Lithography Beam 19 a then irradiates a PDsystem 4 which comprises a number of plates with a plurality of openings(also referred to as apertures). The PD system 4 is held at a specificposition in the path of LB, which thus irradiates the plurality ofapertures and/or openings and is split into a number of beamlets 51 and52.

Some of the apertures/openings are “switched on” or “open” so as to betransparent to the incident beam in the sense that they allow theportion of the beam that is transmitted through it, i.e. the beamlets51, to reach the target; the other apertures/openings are “switched off”or “closed”, i.e. the corresponding beamlets 52 cannot reach the target.Thus, effectively these apertures/openings are non-transparent (opaque)to the beam. Thus, the Lithography Beam 19 a is structured into aPatterned Beam 19 b, emerging from the PD system 4. The pattern ofswitched on apertures is chosen according to the pattern to be exposedon the substrate 16 covered with charged-particle sensitive resist 17.It has to be noted that the “switching on/off” of the apertures/openingsis usually realized by a suitable type of deflection means provided inone of the plates of the PD system 4: “Switched off” beamlets 52 aredeflected off their path (by sufficient albeit very small angles) sothey cannot reach the target but are merely absorbed somewhere in thelithography apparatus, e.g. at an absorbing plate 11.

The pattern as represented by the patterned beam 19 b is then projectedby means of an electro-magneto-optical projection system 5 onto thesubstrate 16 where the beam forms an image of the “switched-on”apertures and/or openings. In accordance with various embodiments, theprojection system 5 may implement a demagnification of, for instance,200:1 with two crossovers c1 and c2. In many embodiments the substrate16 may be a 6″ mask blank or a silicon wafer covered with a particlesensitive resist layer 17. The substrate is held by a chuck 15 andpositioned by a substrate stage 14 of the target station 6.

The information regarding the pattern to be exposed is supplied to thePD system 4 by the data path realized by means of an electronic patterninformation processing system 18. The data path is explained furtherbelow in section “Datapath.”

In accordance with many embodiments the projection system 5 may includea number of consecutive electro-magneto-optical projector stages 10 a,10 b, 10 c, which preferably include electrostatic and/or magneticlenses, and possibly other deflection means. The projection system 5employs a demagnifying imaging through crossovers c1, c2. Thedemagnification factor for both stages is chosen such that an overalldemagnification of several hundred results, e.g. 200:1 reduction. Ademagnification of this order is in particular suitable with alithography setup, in order to alleviate problems of miniaturization inthe PD device.

In the whole projection system 5, provisions may be made to extensivelycompensate the lenses and or deflection means with respect to chromaticand geometric aberrations. As a means to shift the image laterally as awhole, i.e. along a direction perpendicular to the optical axis 19,deflection means 12 a, 12 b, and 12 c may be provided in the condenser 3and projection system 5. The deflection means may be realized as amulti-pole electrode system which is either positioned near the sourceextraction system 8 or one of the crossovers c1 and c2, as shown in FIG.1 with the deflection means 12 b, or after the final lens 10 c of therespective projector, as in the case with the stage deflection means 12c in FIG. 1. In many embodiments, a multipole electrode arrangement isused as deflection means both for shifting the image in relation to thestage motion and for correction of the imaging system in conjunctionwith the charge-particle optics alignment system. These deflection means10 a, 10 b, 10 c are not to be confused with the deflection array meansof the PD system 4 in conjunction with the stopping plate 11, as thelatter are used to switch selected beamlets of the patterned beam 19 b“on” or “off”, whereas the former only deal with the particle beam as awhole. In some embodiments a solenoid 13 may be used to rotate theensemble of programmable beams providing an axial magnetic field.

Turning now to FIG. 2 which illustrates an exemplary embodiment of a PDsystem 4. The embodiment of a PD system 4, may comprise three platesstacked in a consecutive configuration: An “Aperture Array Plate” (AAP)20, a “Deflection Array Plate” (DAP) 30 and a “Field-boundary ArrayPlate” (FAP) 40. It is worthwhile to note that the term ‘plate’ refersto an overall shape of the respective device, but does not necessarilyindicate that a plate is realized as a single plate component eventhough the latter is usually the preferred way of implementation; still,in certain embodiments, a ‘plate’, such as the aperture array plate, maybe composed of a number of sub-plates. The plates are preferablyarranged parallel to each other, at mutual distances along the Zdirection which is represented by the vertical axis in FIG. 2.

In various embodiments the flat upper surface of AAP 20 forms a definedpotential interface to the charged-particle condenseroptics/illumination system 3. The AAP may, for example be made from asquare or rectangular piece of a silicon wafer (approx. 1 mm thickness)21 with a thinned center part 22. The plate may be covered by anelectrically conductive protective layer 23 which will be particularlyadvantageous when using hydrogen or helium ions further illustrated inU.S. Pat. No. 6,858,118 which disclosure is incorporated herein byreference. When using electrons or heavy ions (e.g. argon or xenon), thelayer 23 may also be of silicon provided by the surface section of 21and 22, respectively, so that there is no interface between layer 23 andthe bulk parts 21, 22.

In accordance with many embodiments the AAP 20 may comprise a pluralityof apertures 24 formed by openings traversing the thinned part 22. Theapertures 24 are arranged in a predetermined arrangement within anaperture area provided in the thinned part 22, thus forming an aperturearray 26. The arrangement of the apertures in the aperture array 26 maybe, for instance, a staggered arrangement or a regular rectangular orsquare array. In various embodiments, the apertures 24 are realizedhaving a straight profile fabricated into the layer 23 and a“retrograde” profile in the bulk layer of the AAP 20 such that thedownward outlets 25 of the openings are wider than in the main part ofthe apertures 24. Both the straight and retrograde profiles can befabricated with state-of-the-art structuring techniques such as reactiveion etching. The retrograde profile strongly reduces mirror chargingeffects of the beam passing through the opening.

As illustrated in FIG. 2 according to various embodiments the DAP 30 maybe a plate provided with a plurality of openings 33, whose positionscorrespond to those of the apertures 24 in the AAP 20. Additionally, theopenings 33 may be configured with electrodes 35, 38 configured fordeflecting the individual beamlets passing through the openings 33selectively from their respective paths. The DAP 30 can, for instance,be fabricated by post-processing a CMOS wafer with an ASIC circuitry. Inaccordance with some embodiments the DAP 30 may be of a square orrectangular shape and comprise a thicker part 31 forming a frame holdinga center part 32 which has been thinned (but may be suitably thicker ascompared to the thickness of the tinned part 22). The aperture openings33 in the center part 32 are wider compared to 24 (by approx. 2 μm ateach side for instance). In some embodiments CMOS electronics 34 may beutilized to control the electrodes 35, 38, which are provided by meansof MEMS techniques. In accordance with various embodiments each opening33, may contain a “ground” electrode 35 and a deflection electrode 38adjacent thereto. The ground electrodes 35 may be electricallyinterconnected, connected to a common ground potential, and comprise aretrograde part 36 to prevent charging and an isolation section 37 inorder to prevent unwanted shortcuts to the CMOS circuitry. The groundelectrodes 35 may also be connected to those parts of the CMOS circuitry34 which are at the same potential as the silicon bulk portions 31 and32.

In accordance with some embodiments the deflection electrodes 38 may beconfigured to be selectively applied with an electrostatic potential;when such electrostatic potential is applied to an electrode 38, thiswill generate an electric field causing a deflection upon thecorresponding beamlet, deflecting it off its nominal path. Additionally,the electrodes 38 may have a retrograde section 39 in order to avoidcharging. Each of the electrodes 38 is connected at its lower part to arespective contact site within the CMOS circuitry 34.

In many embodiments the ground electrodes 35 may be higher than theheight of the deflection electrodes 38 in order to suppress cross-talkeffects between channels. Although the electrodes 35 and 38 areillustrated in a specific configuration, it should be understood thatthey may take on any suitable configuration for example the electrodesmay face upstream rather than downstream as illustrated in FIG. 2.

The arrangement of a PD system 4 with a DAP 30 shown in FIG. 2 is onlyone of several possibilities. In a variant (not shown) the ground anddeflection electrodes 35, 38 of the DAP may be oriented upstream (facingupward), rather than downstream. Further DAP configurations, may beutilized, such as those described in U.S. Pat. No. 8,198,601 whosedisclosure is incorporated herein by reference.

In accordance with various embodiments the third plate 40 serving as FAPmay have a flat surface facing the first lens part of the down-streamdemagnifying charged-particle projection optics 5 and thus provides adefined potential interface to the first lens 10 a of the projectionoptics. The thicker part 41 of FAP 40 may be a square or rectangularframe made from a part of a silicon wafer. The FAP 40 may furthercomprise a thinned center section 42. In accordance with manyembodiments the FAP 40 may be provided with a plurality of openings 43which correspond to the openings 24, 33 of the AAP 20 and DAP 30 but arewider as compared to the latter.

In accordance with many embodiments the PD system 4, and in particularthe first plate of it, the AAP 20, may be illuminated by a broad chargedparticle beam 50 (herein, “broad” beam means that the beam issufficiently wide to cover the entire area of the aperture array formedin the AAP), which is thus divided into many thousands ofmicrometer-sized beamlets 51 when transmitted through the apertures 24.The beamlets 51 will traverse the DAP and FAP unhindered.

As already mentioned, whenever a deflection electrode 38 is poweredthrough the CMOS electronics, an electric field will be generatedbetween the deflection electrode and the corresponding ground electrode,leading to a small but sufficient deflection of the respective beamlet52 passing therethrough (FIG. 2). The deflected beamlet can traverse theDAP and FAP unhindered as the openings 33 and 43, respectively, are madesufficiently wide. However, the deflected beamlet 52 is filtered out atthe stopping plate 11 of the sub-column (FIG. 1). Thus, only thosebeamlets which are unaffected by the DAP will reach the substrate.

The ensemble of (unaffected) beamlets 51 as formed by AAP may beprojected to the substrate with a predefined reduction factor R of theprojection charged-particle optics. Thus, at the substrate a “beam arrayfield” (BAF) is projected having widths BX=AX/R and BY=AY/R,respectively, where AX and AY denote the sizes of the aperture arrayfield along the X and Y directions, respectively. The nominal width of abeamlet at the substrate (i.e. aperture image) is given by bX=aX/R andbY=aY/R, respectively, where aX and aY denote the sizes of the beamlet51 as measured along the X and Y directions, respectively, at the levelof the DAP 30. Thus, the size of a single aperture image formed on thetarget is bX×bY

The reduction factor of the demagnifying charged-particle optics 5, asillustrated in FIG. 1, may be chosen in accordance with many embodimentsin view of the dimensions of the beamlets and their mutual distance inthe PD device 4 and the desired dimensions of the structures at thetarget. This will allow for micrometer-sized beamlets at the PD systemwhereas nanometer-sized beamlets are projected onto the substrate.

In many embodiments the beamlets 51 and 52 as represented in FIGS. 1 and2, equate to a plurality of programmable beamlets. It is worthwhile tonote that the individual beamlets 51, 52 depicted in FIGS. 1 and 2represent a much larger number of beamlets, typically many thousands,arranged in a two-dimensional X-Y array. In accordance with someembodiments there may be multi-beam charged-particle optics with areduction factor of R=200 for ion as well as electron multi-beam columnswith many thousands (e.g., 262,144) programmable beamlets. In someembodiments columns with a BAF of approx. 82 μm×82 μm may exist at thesubstrate.

Pattern Exposure

Turning now to FIG. 3 regarding defining the pattern to be exposed onthe target. In many embodiments a pattern image 27A to be produced onthe target 16 is defined by the PD system 4. The target surface coveredwith the charged-particle sensitive resist layer 17 may comprise one ormore areas 27C to be exposed. Generally, the pattern image 27A exposedon the target has a finite size y0 which is usually smaller than thewidth of the area 27C to be exposed. Therefore, a scanning stripeexposure strategy may be utilized, where the target is moved under theincident beam, thus changing perpetually changing the position of thebeam on the target. It is emphasized that for the purpose of theinvention only the relative motion of the pattern image 27A on thetarget is relevant. In many embodiments the relative movement of thepattern image 27A over the target area 27C may form a sequence ofexposure stripes s1, s2, s3, . . . sn having the same width as thepattern image 27A. The complete set of stripes covers the total area ofthe substrate surface. In various embodiments the scanning direction 27Bmay be uniform or may alternate from one stripe to the next.

Turning now to FIG. 4, many embodiments of the invention may havevarious image patterns 28A as illustrated by the pixel 28B pattern ofFIG. 4. In accordance with many embodiments the pixel 28B may be exposedwith varying levels of intensity thus producing an image level differentin a variety of pixels, which is best illustrated by the table in FIG.4. 401, 402, and 403 illustrate the various levels of intensity inaccordance with some embodiments. The full gray level 401 can be seen invarious pixels 28C while a reduced gray level can be seen in otherpixels 28D. Thus the “switched on” beamlets as determined by the PDsystem 4 and the Pattern Information Processing System 18, may becapable of exposing the substrate to a variety of intensity levels toproduce the desired image. The number and intensity of pixels exposed atany given time during the process may vary as the number of aperturescapable of being “switched on” at a given time is predetermined by thephysical parameters of the PD system.

In accordance with many embodiments the intensity or varying level ofwhich the pixel is exposed may be determined by the sequence ofapertures activated to produce the pattern on the desired pixellocation. For example, while the substrate 16 moves, the same imageelement corresponding to a pattern pixel 28B on the target may beexposed many times by the images of a sequence of apertures.

The image pattern may be shifted through the apertures of the PD system.In some embodiments, for example, all apertures may be switched on whensuch apertures are directed to a specific pixel location. The resultwould be the maximum exposure level to that pixel thus producing a“white” shade. Yet in many embodiments the number of “switched on”apertures may vary thus producing a variety of exposure dose levels;accordingly producing a variety of gray levels on the substrate. In someembodiments the dose level may be minimum equating to a “black” shade.Thus in an actual pattern not all pixels are exposed to the full dose ofthe aperture array plate due to various apertures being “switched off.”

In some embodiments the dose level is regulated by reducing the durationof unblanked exposure for the apertures involved. Thus, the exposureduration of one aperture image may be controlled by a discrete number ofgray levels; each of which represents a particular dose to be applied onthe substrate/target, e.g. 0, 1/(n_(Y)-1) . . . , i/(n_(Y)-1), . . . , 1with n_(Y) being the number of available “pixel gray levels” and i aninteger (“gray index”, 0≤i≤n_(Y)). Generally, however, the doseincrements need not be equidistant and form a non-decreasing sequencebetween 0 and 1. The exposed aperture image may be the manifestation ofone of a given numbers of gray shades that correspond to zero and themaximum exposure duration and dose level.

FIG. 5 illustrates an arrangement of apertures in the aperture field ofthe PD device, in accordance with various embodiments of the invention.Aperture images 53A as may be projected to the target are illustrated indark. The main axes X and Y correspond to the direction of advance ofthe target motion (scanning direction 27B) and the perpendiculardirection, respectively. Each aperture image has widths bX and bY alongthe directions X and Y respectively. The apertures are arranged alonglines and rows having MX and MY apertures, respectively, with the offsetbetween neighboring apertures in a line and row being NX·bX and NY·bYrespectively. In accordance with many embodiments based on the layout ofthe apertures each aperature image may have a resulting conceptual cell53B having an area of NX·bX·NY·bY, and the aperture arrangement containsMX·MY cells arranged in a rectangular way. For simplicity the conceptualcell may be referred to as an “exposure cells”. In accordance with manyembodiments the complete aperture arrangement, as projected onto thetarget, has dimensions of BX=MX·NX·bX by BY=MY·NY·bY. In someembodiments the grid may assume a square shape as a special case of arectangular grid, and set b=bX=bY, M=MX=MY, and N=NX=NY with M being aninteger. In such configurations an “exposure cell” 53B has a size ofN·b×N·b on the target substrate.

Turning now to FIG. 6A, in accordance with many embodiments the pitchbetween two neighboring exposure positions may be denoted as e. Ingeneral, the distance e can be different from the nominal width b of anaperture image. In some embodiments b=e, which is illustrated in FIG.6A. FIG. 6a in accordance with various embodiments illustrates anarrangement of exposure cells 53B in a 2×2 pattern where one apertureimage 54A covers (the nominal position of) one pixel. In otherembodiments, as illustrated in FIG. 6B, e may be a fraction b/o of thewidth b of the aperture image, with o>1 being preferably (but notnecessarily) an integer which we also refer to as the oversamplingfactor. Such examples are further illustrated by U.S. Pat. No. 8,222,621and U.S. Pat. No. 7,276,714 which disclosures are incorporated herein byreference. In this case the aperture images, in the course of thevarious exposures, will spatially overlap, allowing a higher resolutionof the placement of the pattern to be developed. It follows that eachimage of an aperture will, at one time, cover multiple pixels, namely o²pixels. The entire area of the aperture field as imaged to the targetwill comprise (NMo)² pixels. From the point of view of placement ofaperture image, this oversampling corresponds to a so-called placementgrid which is different (since it is finer in spacing) than what wouldbe necessary to simply cover the target area.

FIG. 6B further illustrates an exemplary embodiment of an oversamplingof o=2 combined with placement grids, namely, the image of an aperturearray with an exposure cell C4 having parameters o=2, N=2(“double-grid”). Thus, on each nominal location (small square fields inFIG. 6B) four aperture images 55A (dashed lines) are printed, which areoffset on a regular grid by pitch e in both X and Y directions. Whilethe size of the aperture image still is of the same value b, the pitch eof the placement grid is now b/o=b/2. The offset to the previous nominallocation (offset of the placement grid) is also of size b/2. At the sametime, the dose and/or the gray shade of each pixel may be adapted(reduced), by choosing a suitable gray value for the aperture image thatcover the respective pixel. As a result, an area of size b×b is printedbut with an enhanced placement accuracy due to the finer placement grid.Direct comparison of FIG. 6B with FIG. 6A shows that locations ofaperture images are just arranged on a placement grid twice (generally,o times) as fine as before, while the aperture images themselvesoverlap. The exposure cell C4 now contains (No)² locations (i.e.,“pixels”) to be addressed during the write process and thus, by a factorof o², more pixels than before. Correspondingly, the area bi1 with thesize of an aperture image b×b is associated with o²=4 pixels in the caseof oversampling with o=2 in FIG. 6B. Of course, o may take any otherinteger value as well, in particular 4 (“quad-grid”, not shown) or 8, oralso a non-integer value greater one, such as °2=1.414.

In accordance with many embodiments an exposure scheme of the pixels,which is suitable for the invention is illustrated in FIG. 7. Asillustrated in FIG. 7 is a sequence of frames, with increasing time fromtop (earlier) to bottom (later). The parameter values in this figure areo=1, N=2; also, a rectangular beam array is assumed with MX=8 and MY=6.In some embodiments, the target may move continuously to the left,whereas the beam deflection is controlled with a seesaw function asshown on the left side of FIG. 7. During each time interval of lengthT1, the beam image stays fixed on a position on the target(corresponding to a position of a “placement grid”). Thus, the beamimage is shown to go through a placement grid sequence p11, p21, p31.One cycle of placement grids is exposed within a time intervalL/v=NMb/v, by virtue of the target motion v. The time T1 for exposure ateach placement grid corresponds to a length L_(G)=vT1=L/(No)²=bM/No²,which we call “exposure length.”

In many embodiments the beamlets are moved over the distance of L_(G)during the exposure of one set of image elements together with thetarget. In other words, all beamlets maintain a fixed position withregard to the surface of the substrate during the time interval T1.After moving the beamlets with the target along distance L_(G), thebeamlets are relocated to start the exposure of the image elements ofthe next placement grid. After a full cycle through the positions p11 .. . p31 of a placement grid cycle, the sequence starts anew, with anadditional longitudinal offset L=bNM parallel to the X direction(scanning direction). At the beginning and at the end of the stripe theexposure method may not produce a contiguous covering, so there may be amargin of length L that is not completely filled.

In various embodiments an overlapping stripe (“multi-pass”) strategy forerror reduction may be used. Similar strategies are described in U.S.Pat. No. 9,053,906 B2 which disclosure is incorporated herein byreference. An exemplary embodiment (“double-pass”) is illustrated inFIGS. 8A and 8B, which show an exemplary sub-area of the target to beexposed in two passes ps1, ps2. In the first pass ps1 the stripes s11,s12, s13 are exposed in consecutive order, thus exposing the pixelsbelonging to a partial grid G1 (the number of pixels within each of thestripes is reduced in the depiction of FIGS. 8A and 8B for the sake ofclarity and may be higher in typical embodiment). In FIG. 8A, letters A,C, E denote the pixels which are exposable through stripes s11, s12, ands13, respectively. The stripes s11-s13 of one pass are preferablylocated side-by-side, so as to produce a continuous grid over the areaon the target. In this way, the stripes, each having individual widthy0, may cover the total width Ry of the area Rr to be exposed along theY direction (i.e., across the scanning direction sd). In manyembodiments, the stripes s11-s13 may extend to either side of the areashown, and the first pass ps1 may continue with further stripes (notshown) after the stripe s13 has been imaged. After completion of allstripes of the first pass ps1, the stripes of another pass ps2 areperformed, as illustrated in FIG. 8B.

As illustrated in FIG. 8B, the stripes s21, s22 may expose pixels formedwithin the second partial grid G2. FIG. 8B shows two stripes s21, s22,which expose the pixels denoted by letters B and D, respectively. Thus,each pass ps1, ps2 is associated with one of the partial grids G1, G2 ofpattern pixels which are exposable during the respective pass. Takentogether, the pixels of the grids G1, G2 combine to the completeplurality of pattern pixels in the region which is to be exposed. Inother words, the second pass ps2 exposes those pixels which are left outin the first pass ps1, and vice versa. With regard to the Y axis theexposure stripes of different passes are mutually overlapping,preferably in a regular manner wherein the overlapping stripes, forinstance of stripes s11 and s21, differ by a transversal offset Y1 alongthe Y direction (which is the direction across the orientation of thestripes, identical to the scanning direction). For exposing the firsthalf of the stripe s11, and to also cover this part of the total widthRy, an additional ‘edge stripe’ s20 (not indicated in the pixel pattern)may be performed, in which only the upper half of the pixels areexposed, while the lower half of the pixels are kept switched-off alongthe entire length of the stripe s20. In accordance with many embodimentsof the invention there may be more than two passes; for instance, in a“quad-pass” writing strategy, four partial grids written in four passesmay be combined to form the complete plurality of pattern pixels.Further details concerning the exposure of the pixels through exposurestripes and partial grids are described in U.S. Pat. Pub. No.2016/0276131 A1 which disclosure is incorporated herein by reference.

Turning now to FIG. 9A, a graphical illustration of the ideal intensityprofile 71 for a line of a width 30 nm, in the idealized case of zeroblur is presented. When using “quad-grid” (o=4) multi-beam exposure theoverlap is a quarter of the beam size. Thus, for the case of 20 nm beamsize the physical grid size is 5 nm. A discrete dose level can beassigned to each area of the physical grid, which may be 5 nm×5 nm insome embodiments. The line 72 in FIG. 9A indicates the superposition ofthe intensity (or total dose) as it is composed by the overlappingexposure spots with discrete dose levels assigned to the pixel positionsfor generating the 30 nm line, whereas for better visibility the blurhas been set to zero (so that the dose distribution of a single exposurespot becomes a rectangle). If the blur has a realistic value, the stepfunction at the edge of the rectangle is convoluted with a Gaussianfunction, which eventually transforms to a Gaussian shape. In that sensethe line 72 can be seen as superposition of Gaussian functions at blurzero. In many embodiments the dose level histogram will not besymmetrical in order to position the left and right edge at pre-definedpositions.

In accordance with many embodiments, FIG. 9B represents a graphicalillustration of a simulation for a line of 30.0 nm width, with the leftedge to be positioned at 0.0 nm and the right edge at 30.0 nm. For thesimulation, it was assumed that beam spots of 20 nm are exposed with 5.1nm 1sigma blur (i.e., 12.0 nm FWHM blur). The intensity profile 76 isformed by overlapping the profiles of the exposure spots 73, 74, and 75.The dose level of the leftmost exposure spot 74 is adjusted such thatthe 30 nm line starts at the desired start position 77, i.e. at 0 nm.The dose level of the rightmost exposure spot 75 is adjusted such thatexposed line ends at position 78 at 30.0 nm. As can be seen in FIG. 9B,in accordance with “quad-grid” exposure, the overlap of the exposurespots 73, 74, 75 is a quarter of the beam size, i.e. 5 nm.

FIGS. 9C and 9D illustrate how the invention enables the MBW device towrite lines with precise edge definitions in accordance with manyembodiment of the invention. In each figure, the top frame shows theedge position error vs. line width, the middle frame illustrates theintensity profile, and the bottom frame shows the edge positiondeviation when enhancing the exposure dose by 10% vs. line width. FIG.9C shows the intensity profile obtained for a 31.4 nm line width, andFIG. 9D for a 40.0 nm line width. Using the MBW with 20 nm beam size andquad-grid exposure (5 nm physical grid size), the line width of thestructure generated by the exposure can be changed in steps of 0.1 nm.Because of the integer dose levels, there may be slight deviations fromthe 0.1 nm address grid. These deviations are indicated as “edgeposition error” (top frames), as functions of the desired line width, in0.1 nm steps between 30.0 nm and 40.0 nm. As can be seen the deviationsare within ±0.05 nm. Furthermore, the change of edge position with 10%change of dose is only approx. 1 nm, varying only slightly with changeof line width as shown in the bottom frames. In other words, since thedose is controlled in a MBW to better than 1%, the change of edgeposition with 1% change of dose is within approx. one atomic layer.

In accordance with many embodiments of the invention dose variations maybe utilized in the MBMW to achieve edge placement with sub-pixelprecision. FIG. 10 illustrates the exposure of one exposure spot with amaximum dose level. In the exemplary case of a 4-bit coding, there are16 dose levels (0, 1, 2, . . . 15), i.e. the maximum dose level is thesum of 15 dose level increments 64.

Turning now to FIGS. 11A, 11B, and 11C, intensity profile diagramsillustrating how the multi-beam exposure methods can achieve a finepositioning of structure feature with resolution smaller than the gridsize. In the intensity profile diagrams, like those of FIGS. 11A-C, thediscrete dose levels are visualized as rectangles 64 of uniform height,piled up in a “brick-layer” arrangement; of course, this “brick-layer”depiction is only symbolical and intended to facilitate interpretationof the drawings.

FIG. 11A shows a dose level histogram, for an exemplary embodiment of aline of 30 nm width exposed by means of a 4 bit (i.e., 15 dose levelsper spot) exposure in a quad-grid with a beam spot size of 20nm width.The grid size 62 is ¼ of the linear size of the exposure spots, whichare symbolized as rectangles piled up in a “brick-layer” arrangement,and the resulting dose level distribution 65 is outlined as a bold line.

The line width can be made smaller or larger in very fine steps, whichare smaller than the grid size, in this case the quad-grid size 62.Reducing the line width can be achieved by lowering the dose level ofthe outermost exposure spots and/or omitting exposure spots (the latterwhen the reduction is at least about one half of an exposure spot size).Increasing the line width can be achieved by enhancing the dose level ofthe outermost exposure spots and/or, in particular when the maximum doselevel has been reached, by adding an additional, preferably overlapping,exposure spot. The latter aspect is illustrated in FIG. 11B: an exposurespot 66 having a defined dose level is added, resulting in a dose levelhistogram 67 for the line with larger width compared to 65. By combiningthese effects of decreasing and increasing on either side, there is alsothe possibility to shift the line position in very fine steps. FIG. 11Cillustrates a shift of the line without changing the width, which isachieved by removing dose levels from spot 68 and adding dose levelsfrom spot 69, resulting in the dose level histogram 70 which correspondsto a line shifted to the right as compared to the line of FIG. 11A.

The intensity profiles illustrated in FIGS. 11A-C are shown along the Xdirection of the target plane. It should be understood that themulti-beam exposure methods illustrated here may be applied to linesalong other directions as well, and fine positioning can be achieved forlines at any angle on the target plane.

Dose Inhomogeneity Correction

U.S. Pat. Pub. No. 2015/0347660 A1, which disclosure is incorporatedherein by reference, illustrates the current transmitted by each beamlet(or aperture) may not be uniform but may vary, mainly as a function ofthe distance to the optical axis 19 (FIG. 1). This effect is due toimperfections in the charged particle source. Without furthercorrections, the dose a pixel may receive will thus vary depending onthe beamlet writing said pixel, leading to systematic edge placementerrors.

FIG. 12 illustrates an exemplary embodiment of a current density map Mp.More precisely, it shows a 8×8 coarse grained map of the deviationα(X,Y) (quantified in percentage [%]) of the current of a single beamletlocated at a position/areal (X,Y) relative to the mean current acrossthe image field. Typically, in the map the current dose values near thecorners of the beam array are either reduced or enhanced with regard tothe average over the map. In the example of FIG. 12 the beam array fieldof 82 μm×82 μm at the target consisted of 512×512=262,144 programmablebeamlets. As shown, an 8×8 matrix of the current dose distribution wasmeasured, wherein each measured value comprises 262,144/64=16,384beamlets used to generate the respective value. The electron sourceunderlying FIG. 12 was of the type of a thermal field emission cathodewith a flat emitter surface (single crystal, e.g. Tungsten or LaB₆).Since the electrons are emitted from a larger surface (typically 20 μm),it is unavoidable due to mechanical imperfection (e.g. alignment ofemitter surface with respect to anode) or local differences in theextraction field strength, that the angular current density variesacross the emitter.

In accordance with many embodiments dose variations may be corrected byupdating the dose corresponding to a pixel by dividing by a homogenizing“dose correction factor” q depending on the beamlet writing said pixel,which is given by q=C(1+α), where C=1/[min_([X,Y]) (1+α(X,Y))] is aconstant that fixes the minimum dose inhomogeneity correction factorat 1. (Here the symbol min_([X,Y]) is the minimum value among the valueswithin the entire range of interest of X and Y coordinates.) Thiscorrection typically happens on-line as part of the data path.

Data Path

In accordance with many embodiments the MBW integrates a processingsystem 18, as illustrated in FIG. 1, that converts the patterns to bewritten to beamlet dose assignments (as described above), which can beused in the writing process, is referred to as “data path” system. Inaccordance with many embodiments, FIG. 13 shows a flowchart of a datapath 170 in the context of the invention. The data path is preferablyperformed in real time; in a variant, part or all of the calculations ofthe data path may be performed in advance, for instance in a suitablecomputer.

The complete pattern image may comprise a vast amount of image data,which is why for efficient computation of those data a high-speed datapath that generates the pixel data to be exposed, preferably inreal-time, will be suitable. The pattern to be exposed is typicallydescribed in a vector format, for example as a collection of geometrieslike rectangles, trapezoids or general polygons, which typically offersbetter data compaction and therefore reduces the requirements on datastorage. Therefore, in accordance with many embodiments, the data pathmay consist of three major parts:

-   -   a vector-based physical correction process (step 160),    -   rasterization processes to translate the vector to pixel data        (steps 161 to 164), and    -   buffering of pixel data for temporary storage for the writing        process (steps 165 and 166).

As illustrated in FIG. 13, the data path starts upon being supplied apattern PDATA to be exposed at step 160. In step 160, generally, thepattern PDATA to be exposed may be split into a large number of smalldata chunks, possibly with geometric overlaps. Corrections that can beapplied in the vector domain (e.g. proximity effect correction) may becarried out to all chunks independently, possibly in parallel, and theresulting data is sorted and coded so as to improve computation speed ofsubsequent steps. The output is a collection of chunks where all chunkscontain a collection of geometries.

Stage 161 as illustrated in FIG. 13 may be referred to as theRasterization stage: RAST. The geometries of every chunk are convertedinto rasterized pixel graphics. In this step, each pixel may be assigneda floating-point gray scale intensity depending on the geometric overlapof the corresponding surface of the raster-grid cell with the pattern tobe exposed, i.e. the entity of all associated chunks. Thisfloating-point intensity represents the ideal physical exposure dose tobe delivered onto the target at the respective pixel location.Furthermore, every pixel that is completely inside a geometry may beassigned the maximal intensity, whereas the intensity of pixels thatcrosses an edge of a geometry is weighted by the fraction of the area ofthe pixel that is covered by the geometry. This method implies a linearrelation between the area of the geometry and the total dose after therasterization.

Stage 162 as illustrated in FIG. 13 may be referred to as thePixel-to-beamlet assignment stages: ASSIGN. In this step, given aparticular write sequence, it is determined which pixel will be writtenby which beamlet.

Stage 163 as illustrated in FIG. 13 may be referred to as the Pixelbased corrections stage: CORR1. In this step, all corrections that canbe applied in the pixel domain may be performed. These correctionscomprise compensation of deviations from a uniform current density ofthe beam 50 over the aperture field, as described earlier and furtherillustrated in U.S. Pat. No. 9,495,499; whose disclosure is incorporatedherein by reference. Additionally, the corrections may be for individualdefective beam deflectors in the DAP 30. Further illustration isprovided in U.S. Pat. No. 9,269,543; which disclosure is incorporatedherein by reference. Pixel based corrections are realized by modifyingthe floating-point intensity of each individual pixel. This is beingdone with respect to the Pixel-to-beamlet assignment of Stage 162, whichmakes it possible to define and apply a compensation dose-factor q (or,equivalently a dose-shift s) for each pixel depending on by whichbeamlet it is written, and/or by which beamlets the neighboring pixelsare written.

Stage 164 as illustrated in FIG. 13 may be referred to as theQuantization stage: QUANT. The quantization process converts thepossibly corrected, floating-point intensity of each pixel into aquantized (or equivalently ‘discrete’) gray level, given a predeterminedgray value scale.

Stage 165 as illustrated in FIG. 13 may be referred to as a second pixelbased correction stage or CORR2 may be for further optional pixel basedcorrections in the gray-level pixel data domain (not part of the presentinvention).

Stage 166 as illustrated in FIG. 13 may be referred to as Pixelpackaging, PPACK. The pixel image obtained from stage 164 is sortedaccording to the placement grid sequence and sent to a pixel buffer PBUFwhich is provided in the processing system 18 of the writer tool (FIG.1). The pixel data is buffered until a sufficient amount of data,typically at least the length of a stripe, is present, which triggersthe exposure of the stripe (see FIG. 7). The data is taken out of thebuffer during the writing process. After the stripe has been written,the process described above starts anew for the pattern data of the nextregion, such as the next stripe.

Dose-Level Quantization

The present invention pertains to the QUANT stage 164 of the data path,which converts the floating-point (or equivalently high-resolution)intensity data into a quantized (i.e. discrete) gray level scale. In atypical realization of the invention the gray-level data is finallyrepresented by a low-bit code, i.e., a code expressed through a smallnumber of data bits. For instance, in a scenario where every pixel isdescribed by 4 bits, pixels that are switched on have 2⁴=16 possibleconfigurations, i.e. n_(Y)=16 dose levels (0, 1, 2, . . . , 15). In arealization where the minimum dose 0% and the maximum dose 100% isequidistantly divided into 16 discrete dose levels, the step between twodose levels is 100%/15=6.67%.

In accordance with various embodiments finer dose-steps may be achievedvia a suitable approach that exploits for oversampling o>1 to improvethe discretization by means of a dithering process. The main principleof altering the dose in steps finer than 6.67% is illustrated in FIGS.14 and 15. In FIG. 14, four neighboring pixels p1, p2, p3 and p4 for theexample of double-grid oversampling (o=2) are shown. Since the pitchbetween neighboring pixels is e=b/2, each overlapping area of sizee²=b²/4 is simultaneously covered by four beamlets. As the individualpixels each carry a 4-bit wide information, there are now 4×15+1=61possible dose levels. Thus, the dose on the substrate can effectively bealtered in steps of 6.67%/4=1.67% in contrast to the 6.67% for theindividual pixels. In FIG. 15, the dose of the overlapping area o1 inthe middle (dashed area) is considered. Starting from dose zero on allfour neighboring pixels cfg1, the dose-level of o1 is increased by one,resulting in configuration cfg2 where the dose in the overlapping areais now 1 out of 4×15=60 possible non-zero dose-level configurations.Thus, the overall dose has increased by only 1/60=1.67%. FIG. 15 showsall possible 4+1=5 dose configurations cfg1, cfg2, cfg3, cfg4, cfg5 ofthe overlapping area for the case of two-dose levels, e.g. the pair 0and 1, for the individual pixels p1, p2, p3 and p4. The skilled personeasily realizes that any of the 60 possible non-zero dose-levels can beobtained by a combination of 4 pixels with 15 non-zero dose-levels. Thefiner gray level scale achievable in the overlapping area will bereferred to as “effective gray levels” in the following.

As the number of overlapping pixels only depends on the oversamplingfactor o, it is straight-forward to compute the number of dose levelsfor any combination of oversampling o and gray-level n-bit resolution.In detail, the number of overlapping pixels is o², resulting ino²×(2^(n)-1)+1 effective gray-levels in steps of 1/(o²×(2n-1)+1).Besides the mentioned cases of oversampling o=2 and bit-resolution n=4,another interesting scenario with respect to the implementation of theapplicant is o=4 (so-called quad-grid-mode) and n=4, wheren_(Y)=4²×(2⁴-1)+1=241 effective dose-levels are available, which can bevaried in steps of 0.4167%. It will be evident to the skilled personthat other combinations of o and n may be suitable depending on theindividual implementation.

A computationally inexpensive algorithm is required which, starting froma desired floating-point pixel intensity, determines a proper discretegray-level assignment for neighboring pixels. Besides the requirement ofbeing computationally inexpensive, this algorithm will have to ensurethat the entire range of o²×(2^(n)-1)+1 effective dose-levels can beexploited.

Quantization Using Ordered Dithering

Due to its ease of calculation and deterministic behavior, ordereddithering is a method particularly suited for dose level discretization.During ordered dithering quantization, for every pixel (aperture imageposition) the fractional gray level value of the nominal dose iscompared against a threshold value in a regular pattern obtained from aBayer index matrix which is used as dithering matrix. The dose is thenrounded up to the next dose step if it surpasses the threshold androunded down otherwise. In general, the relationship between thresholdmatrix T and Bayer index matrix B (which describes the order in whichbeamlets are rounded up for increasing target dose) is given by

$T_{ij} = {\frac{{2B_{ij}} - 1}{2d^{2}}\left( {i,{j = 1},\ldots \mspace{14mu},d} \right)}$

where d is the dithering order, i.e., the size of the dithering matrixB, which is usually quadratic. The dithering order d may be convenientlychosen equal to the oversampling factor o. Given the fundamental Bayermatrix B2 of FIG. 17A, Bayer matrices of arbitrary dimensions which arepowers of two can be calculated recursively, namely, starting from the2×2 matrix B₂=B2 and using the recursion rule

$B_{2n} = \begin{pmatrix}{{4 \times \left( {B_{n} - 1} \right)} + 1} & {{4 \times \left( {B_{n} - 1} \right)} + 3} \\{{4 \times \left( {B_{n} - 1} \right)} + 4} & {{4 \times \left( {B_{n} - 1} \right)} + 2}\end{pmatrix}$

where B_(n) is a Bayer matrix of dimension n×n

A simplified example for the application of a dithering matrix forrounding is presented in FIG. 16, relating to the case of two pixel graylevels (that is, every pixel has 1-bit data; thus, it can only beswitched on or off) and double-dithering (i.e. d=2). The array NP2represents an example of a desired pattern, in which each entry containsa value of the dose to be exposed at the respective area element on thetarget (target dose values, also referred to as nominal dose values). Inthe example shown, the array contains several instances of values 0,0.1, 0.5, and 1. FIG. 17A shows a dithering matrix B2 of size 2×2 ford=2, and FIG. 17B shows the threshold matrix T2 resulting from thedithering matrix B2. The threshold matrix T2 is tiled in the plane in aregular pattern to obtain the threshold pattern TP2 (left-hand part ofFIG. 16). The dimensions of the threshold pattern TP2 will suitablyconform to the dimensions of the desired pattern array NP2 (top of FIG.17). According to the dithering procedure, rounding is achievedcomparing the nominal dose value in each entry of the pattern NP2 withthe corresponding entry of the threshold pattern TP2, resulting in aquantized array QP2, which contains an array of dose values quantized toconform to the available gray values. In this example, the nominal dosevalues of 0.5 (half a pixel gray level) are rounded up and down in analternating pattern, whereas doses of 0.1 are rounded down everywhere.The other dose values which occur in the target dose, i.e. 0 and 1,remain unchanged since they exactly match a pixel gray level

Another example is given in FIGS. 18, 19A, and 19B for the same targetpixel doses y in a pattern array NP4, but using quad-dithering (d=4)with a 4×4 dithering matrix B4 (FIG. 19A), and 4 (2-bit) pixel graylevels. The 2-bit information of one gray value means that a theavailable discrete gray values h form a palette having 2²=4 values, forinstance, 0 (zero), ⅓, ⅔, and 1. Each element will be assigned aquantized value h chosen from the palette based on the original pattern.FIG. 19B shows the threshold matric T4 which is calculated from thedithering matrix B4. In FIG. 18 the resulting threshold pattern TP4 isillustrated. During the process of dithering from the desired patternarray NP4 to the quantized array QP4, the nominal dose values of 0.5 arerounded in an alternating pattern to the next pixel gray levels of ⅓ and⅔, since the remainder of the subtraction 0.5−⅓=⅙, when divided by thestep-size of the gray scale, i.e. ⅓, gives 3/6, which is larger than5/32 and 15/32, but smaller than 20/32 and 17/32. Similarly, half of thepixel dose values of 0.1 are rounded up to ⅓ (since 0.1/(⅓)=0.3 isgreater than 9/32 and 1/32) and the other half are rounded down to 0(since 0.3 is smaller than 19/32 and 25/32). It should be noted that thevalues of the entries shown in the matrices T4 and TP4 are scaled by anoverall factor of 1/32 (indicated outside the respective matrix).

The general procedure for arbitrary dithering order d and bits per pixeln is as follows:

-   -   1. Decompose every nominal dose value into the form y=c*k+r,        where the dividend k is the step-size, i.e. the step width of        the gray scale, as determined by the number of bits n, i.e.        k=1/(2^(n)-1), and where the integer quotient c and (positive        real-valued) remainder r are determined uniquely according to        the Euclidean division theorem. In particular, the quotient c is        a non-negative integer, and the remainder is a non-negative        number r<k.    -   2. Compare the value v=r/k with the associated entry of the        dithering threshold matrix. If this value v is larger than the        entry from the dithering threshold matrix, the pixel is a        assigned the discrete grey-level h=(c+1)*k; whereas if v is less        than or equal to said threshold value, the pixel is assigned the        discrete grey-level h=c*k.

Thus, in the second step, a floating point nominal dose value y (unlessit already coincides with one of the values in the gray scale palette)is either rounded up or down, relative to the discrete grey-level scalewith step-size k.

Ordered Dithering and Dose Corrections

The combination of oversampling, dose corrections, and ordered ditheringcan lead to complex stochastical effects. Various exemplary embodimentsconsider the case of double-grid exposure (o=2) and n_(Y)=16, i.e. 16gray levels (4-bit) for every pixel/beamlet and double-dithering (usingthe dithering matrices of FIGS. 17A+B). As in FIG. 14, an overlappingarea o1 is exposed by four overlapping aperture image positions p1, p2,p3, p4, giving a total of 61 gray levels. Since this corresponds to doseincrements of 1/60=1.67%, the maximal dose error due to quantization is0.84% (½ effective gray level or ⅛ pixel gray level) when using optimalrounding. When using ordered dithering for quantization, this error maybecome larger, particularly in the presence of inhomogeneous beamcurrent and corresponding corrections as described earlier.

FIG. 20 illustrates an exemplary embodiment for the case of homogeneousbeam current. Consider a typical use-case, where a line through theupper half of the overlapping area o1 is to be exposed, as illustratedin the target dose array NP20. The beamlets at pixels p3, p4 are todeliver a maximal dose of 1, and the beamlets at p1, p2 a dose of7.125/15=0.475 to produce a total o1 dose of 44.25/60=0.7375 of themaximal overlap dose 4. Applying the dithering matrix to obtain thequantized array QP20, the pixel p1 is rounded up to the next discretegray level 8, whereas the pixel p2 is rounded down to 7; the pixels b3,b4 remain unchanged. The two roundings combine to an overlap dose errorof 0.75/60=1.25% (which experimentally corresponds to a line edgeplacement error in the order of approx. 0.4 nm).

While in this example, the rounding error is larger than the idealquantization error, it is the worst case scenario when writing a linewith this dithering matrix and homogeneous beamlet doses. Also note thatthis is not a generic error that occurs when using ordered dithering,which means that there are also cases where there is no rounding errorat all. Consider for example the case in FIG. 21. Here, the target dosevalue (array NP21) for the overlapping area o1, namely 45, is exactlymatched when using the ordered dithering process as visible from theresulting quantized array QP21, even though the target dose of pixelsp1, p2 lies between two discrete values; namely 7 and 8.

In the case of inhomogeneous beamlet current the rounding behavior canbe much worse. This is due to the fact that the corrected doses mayalign with the dithering thresholds in an unfavorable way. An example isgiven in FIG. 22, comprising the same target dose values NP20 as in thecase of FIG. 20, but with additional dose inhomogeneity correctionfactors. While the target dose is the same as in FIG. 20, due to thefact that the beamlets carry different amounts of current, the dosesassigned to each pixel have to be adjusted with beamlet-dependent dosefactors DF22 to effectively deliver the target doses DP22. Each pixel isnow assigned an individual corrected dose, which, in some cases, canalign unfavorably with the dithering thresholds. In FIG. 22, the worstpossible rounding behavior is shown in the array NQ22 (all pixels arerounded up), leading to a total dose error of approximately 3.3%(45−43=2 out of 60 non-zero effective gray levels, or, equivalently ½single pixel gray level), which, for the MBMW of the applicant, mayexperimentally correspond to an edge placement error of about 1.32 nm.This dose error also approximately remains in the effective dose (i.e.,accounting for the different beamlet currents).

In accordance with many embodiments, the above scenario can be resolvedby using the same or very similar dose correction values for overlappingpixels which undergo the dithering process. Consider, for example, FIG.23; where, a common dose-correction-factor 0.972 (array DF23 has auniform value) among the neighboring beamlets is applied which preservesthe exact target dose, as can be seen in arrays DP23 and NQ23. That is,in the quantized dose distribution NQ23 the target dose of overlap o1 isstill 43 as before, but with the advantage that when the ordereddithering is applied, no rounding error occurs at all.

FIG. 26 illustrates a plot of the rounding errors (in terms of effectivegray levels) for the target dose values from FIGS. 20 to 23 for therange 0.84 to 1.0 of common dose-correction factors for the fourneighboring, and potentially overlapping pixels. Here, it may beobserved that the worse-case rounding error of two effective gray levelsdoes not occur. Instead, the maximal error is halved to one effectivegray level.

In accordance with many embodiments FIGS. 27A to 35B, illustrate theadvantageous behavior of dose correction factors during dithering byusing a uniform dose correction for each aperture-line along the writedirection (i.e., the scanning direction sd, see FIG. 3). FIG. 27A showsa typical case of a current profile (more exactly, current densityprofile) across the image-field of size 80 μm×80 μm, each valuerepresenting the deviation α(X,Y) (quantified in percentage [%]) of thecurrent of a single beamlet located at the position (X,Y) of arespective area, relative to the mean current across the image field.The values listed in FIG. 27A depict a typical distribution according toa realistic scenario, with a roughly parabolic overall characteristicand a deviation range of several per cent. Corresponding normalizedcorrection dose factors q (see above, Section ‘Dose inhomogeneitycorrection’) are given in FIG. 28A, which are proportional to themultiplicative inverse of the doses from FIG. 27A. FIG. 29A shows thecorrected dose profile: applying the factors from FIG. 28A to themeasured doses shown in FIG. 27A yields a completely flat dose profileof constant value 0.960. Note that the overall dose is now lower by aconstant 4% across the whole image-field. This decrement, however, caneasily regained by increasing the overall source current by thecorresponding amount.

The data in FIGS. 27A to 29A relate to the current profile, whichcorresponds to a (fictitious) pattern profile of uniform gray level y=1.In the case of a realistic pattern profile, where each of the pixelswill receive an individual gray level value y with 0≤y≤1 (nominal dosevalue), the correction dose factors q are used to correct these nominaldose values y so as to compensate for the non-ideal current profile(FIG. 27A). This is done by dividing each nominal dose value y by thevalue q of the respective beamlet (FIG. 28A), so as to obtain acorrected dose value y′=y/q. This correction is made for each beamlet(i.e., each pixel or image element on the target) of the entire imagefield.

In order to avoid that the unfavorable worst-case rounding occurs, onecomputes the averaged dose profile along the scanning direction sd,which in this example is the X-axis. Re-normalized, this yields theeffective dose-values shown in FIG. 27B, which can be corrected via thedose-correction factors given in FIG. 28B. Overall, the meandose-intensity is reduced to the common value 0.974 as shown in FIG.29B. This is another advantage of this aspect of the invention, namelythat the minimum dose correction factor q is larger due to thisaveraging. This has the effect that more effective dose levels areavailable for writing a pattern, because the lower this number is, themore gray-levels are effectively needed fordose-inhomogeneity-correction.

While the worst-case rounding behavior (of two effective gray levels)described earlier only occurs by chance, it may appear systematically ifan overlapping stripe strategy (=multipass) is applied as described inU.S. Pat. No. 9,053,906; which disclosure is incorporated herein byreference. Consider again a double-grid double-dithering strategy withordered dithering discretization as illustrated in FIG. 14. In addition,a double-pass writing strategy as described previously is applied,according to which the pixels p1, p4 will typically be written in onepass, whereas the pixels p2, p3 are written in the other pass. Pixelswritten in the same pass tend to have similar dose factors (as theyoriginate from the same y-position of the charged particle source), orhave already been equalized according to previously introduced method.Due to the structure of the dithering matrix, the pixels p1, p4 are morelikely to be rounded up, whereas p2, p3 tend to be rounded down, leadingto an intricate correlation between the dose factors and the roundingbehavior, which under certain circumstances can introduce systematicedge placement errors across the beam-field when exposing a regularpattern.

An example is given in FIG. 24; the reference symbols correspond tothose of FIGS. 22 and 23 mutatis mutandis. As before, the beamlets areassigned individual dose correction factors q, however, in this case acorrelation between the dose factors and the dithering matrix arises.The solution presented in FIGS. 27 to 29, in which a common dosecorrection factor q is assigned to each aperture line improves thesituation, but not to a satisfactory amount, because pixels p1, p4 andp2, p3 may now be written by beamlets from different aperture rows.Consequently, only two of the four dose factors will be identical. Inthis case, the maximal rounding error is again four times as large asthe ideal quantization error with 3.33% (two effective gray levels). Insome constellations, the error can be additionally increased due to thefact that beamlets from one pass now have the tendency to get roundeddown, whereas for the other pass it is more likely that the beamlet isrounded up. In the example given in FIG. 24, for instance, thehigh-dose-factor beamlets have the tendency to be rounded down andlow-dose-factor beamlets the tendency to be rounded up, leading toobservable systematic CD errors with respect to the Y-position of astripe.

The solution to this problem is presented in accordance with manyembodiments and further illustrated in FIGS. 30A to 32B. First, aneffective dose-profile is computed by averaging the dose profile α(X,Y)(quantified in percentage [%] of the current of a single beamlet locatedat a position (X,Y) relative to the mean current across the image field)according to the (multipass) stripe overlap (compare with FIG. 8A andFIG. 8B). This stripe overlap is determined by the offset Y1 betweenoverlapping stripes, Y1=y0/2. FIG. 30A shows the deviation α(X,Y) of theeffective dose-profile from the mean value in per cent. For thiseffective dose-profile, one then computes the corresponding correctionfactors, as illustrated in FIG. 31A. Optionally, the factors areadditionally equalized along the X-direction, analogously, as for thenon-overlapping stripe-exposure mode; this leads to the effective dosecorrection factors as illustrated in FIGS. 30B and 31B. In particular,using the common correction factors as depicted in FIG. 31B in thedouble-pass mode, where stripes from different passes overlap with 50%of their width (as also shown in FIGS. 8A and 8B), a maximal roundingerror of 1 effective gray level is achieved, since the neighboringpixels from different passes now have the same dose correction factor q,as e.g. depicted in FIG. 25.

It is straightforward to generalize the procedure described above toother scenarios. For instance, the quad-pass variant is illustrated inFIGS. 33A to 35B. Here, the offset Y1′ between overlapping stripes is ¼of the stripe width y0, and every second image-field segment is averagedin Y-direction, corresponding to four passes; in other respects, theFIGS. 33A to 35B correspond to those of FIGS. 30A to 32B, respectively.Note again, that the minimum dose correction factor over the image-fieldbecomes larger the more averaging is performed.

Although various embodiments are presented herein, it should beunderstood that any suitable embodiment may be utilized.

Doctrine of Equivalents

As can be inferred from the above discussion, the above-mentionedconcepts can be implemented in a variety of arrangements in accordancewith embodiments of the invention. For example, though the method forcorrecting the written pattern from a multibeam-writer is described inrelation to the various components of the MBW, other arrangements may becontemplated within the scope of the current disclosure.

Accordingly, although the present invention has been described incertain specific aspects, many additional modifications and variationswould be apparent to those skilled in the art. It is therefore to beunderstood that the present invention may be practiced otherwise thanspecifically described. Thus, embodiments of the present inventionshould be considered in all respects as illustrative and notrestrictive.

What is claimed is:
 1. A method for writing a desired pattern on atarget, comprising: providing a pattern definition device having aplurality of apertures transparent to a source of radiation, directingan illuminating wide beam through the apertures of the patterndefinition device to form a patterned beam consisting of a correspondingplurality of beamlets, illuminating a target with the patterned beamduring a sequence of exposure intervals to form a pattern image on thetarget, wherein the pattern image is configured to form a plurality ofpattern pixels on the target wherein the plurality of pattern pixelscorrespond to at least a portion of the plurality of apertures, andwherein during the sequence of exposure intervals, at least a portion ofthe plurality of apertures are selectively controlled such that theplurality of pattern pixels are exposed to a respective dose amount,generating a relative movement between the target and the patterndefinition device to produce a stepwise movement of the pattern image onthe target along a path over an exposure region, said path comprising aplurality sections which extend along a scanning direction, wherein theplurality of sections correspond to a plurality of exposure stripes thatcollectively cover the entirety of said exposure region over sequentialexposures, wherein the exposure stripes are mutually overlapping andoffset from each other in a direction transverse to the scanningdirection, such that exposure region is exposed by at least twodifferent exposure stripes at different transversal offsets, andcalculating, for each pixel, a corrected dose amount by dividing thevalue of the nominal dose amount by a correction factor, wherein thesame correction factor is used with pixels written by beamlets locatedat positions which differ only by said transversal offsets ofoverlapping stripes.
 2. The method of claim 1, wherein during the stepof calculating a corrected dose amount for each pixel, an availablecurrent density at the respective pixel is determined, wherein saidmaximum available current density is determined as the actual currentdensity of the irradiating beam radiated through the aperturecorresponding to the respective pixel, said correction factor of therespective pixel is calculated as the ratio of said available currentdensity to the minimum current density across the overall beam arrayfield, and correction factors are averaged among those pixels that arelocated at positions which differ only by said transversal offsets ofoverlapping stripes.
 3. The method of claim 1, further comprisingmultiplicative renormalization of the correction factors, using arenormalizing factor chosen such that one of the largest value and thesmallest value of the correction factors is renormalized to
 1. 4. Themethod of claim 1, wherein the step of calculating a corrected doseamount for each pixel comprises calculating, for each pixel in a row ofpixels parallel to the scanning direction within a respective exposurestripe, corrected dose amounts by dividing the values of the doseamounts by a row correction factor, wherein said row correction factoris uniformly applied to all pixels of a row of pixels.
 5. The method ofclaim 4, wherein said row correction factor is calculated for arespective row of pixels based on the values of current dose actuallyradiated through a series of apertures, said series of aperturescontaining all apertures within the pattern definition device whichimpart dose amounts to the respective row of pixels, wherein the rowcorrection factor of a row of pixels is calculated as the ratio ofactual current dose of an aperture, as averaged over the correspondingseries of apertures, to a nominal current dose value assumed to beconstant over the plurality of apertures of the pattern definitiondevice.
 6. The method of claim 1, wherein said region where a beamexposure is to be performed is composed of a plurality of pattern pixelsarranged in a regular arrangement, said region having a total width asmeasured across said scanning direction, said exposure stripes withinsaid region running substantially parallel to each other along saidscanning direction and having uniform widths as measured across saidscanning direction.
 7. The method of claim 6, wherein the exposurestripes are mutually overlapping, the position of the stripes differingby a transversal offset in a direction across the scanning direction,wherein the row correction factors of rows of pixels are averaged overthose rows of pixels which are offset to each other by said transversaloffset.
 8. The method of claim 1, wherein the correction factor variesbetween groups of pixels where said groups of pixels differ by an offsetwhich does not correspond to a transversal offset of overlappingstripes.
 9. The method of claim 1, including computing an exposurepattern suitable for exposing the desired pattern on a target using saidpattern definition device for writing said desired pattern by exposing amultitude of pixels within said region on the target, wherein duringexposing the desired pattern on a target: in said pattern definitiondevice said plurality of blanking apertures is arranged in apredetermined arrangement defining mutual positions of the blankingapertures, each blanking aperture being selectively adjustable withregard to a dose value to be exposed through the respective blankingaperture onto a corresponding aperture image on the target during arespective exposure interval, said dose value taking a respective valuein accordance with a discrete palette, said discrete palette including anumber of gray values forming a scale ranging from a minimum value to amaximum value, during a writing process of said desired pattern, asequence of exposure intervals is made, wherein in each exposureinterval the blanking apertures are imaged onto the target, thusgenerating a corresponding plurality of aperture images, wherein theposition of aperture images is kept fixed relative to the target at theposition of a pixel during an exposure interval, but between exposureintervals the position of aperture images is shifted over the target,thus exposing the multitude of pixels on the target, and the apertureimages are mutually overlapping on the target, and the aperture imageshave a nominal width which is greater than the distance between pixelpositions of neighboring aperture images on the target, by anoversampling factor greater than one, wherein computing the exposurepattern comprises: determining the discrete palette, providing thedesired pattern and calculating a nominal exposure pattern as a rastergraphics defined on the multitude of pixel elements, said nominalexposure pattern being suitable to create a nominal dose distribution onthe target realizing contour lines of the desired pattern and includingfor each pixel element a respective nominal dose value, and determining,for each pixel element, a discrete value which approximates the nominaldose value of the respective pixel element, said discrete value beingselected from the discrete palette, wherein determining the discretevalues includes employing ordered dithering using a dither matrix of apredefined size.
 10. The method of claim 9, wherein the dither matrix isa Bayer matrix.
 11. A pattern definition device comprising: a pluralityof apertures transparent to a source of radiation, a data processingunit having at least one input terminal and in communication with theplurality of apertures transparent to a source of radiation wherein thedata processing unit is configured to receive a set of instructionsdefining a desired pattern image to be exposed on a target area, whereinat least a portion of the plurality of apertures correspond to aplurality of pattern image pixels on the target area and the at least aportion of the plurality of apertures are configured to expose thepattern image pixels to a respective dose amount in accordance with thedesired pattern image, and wherein the data processing is furtherconfigured to calculate a correction dose needed for each of the patternimage pixels to correct for a pattern beam overlap by dividing a valueof the nominal dose amount by a correction factor dose, and wherein thedata processing unit is further configured to communicate the correctiondose to the plurality of apertures.